In the case with \(\phi = {\bf 1}_{[0,1]}\) , these results
were already proved in [1]}, but the method here provides
an alternative and possibly shorter proof (the proof in [1]}
relies on a lengthy RSW argument from [3]}, as well as not
working for general \(\phi \) ).
When \(\phi = {\bf 1}_{[0,1]}\)  it is known [3]}
that \(\theta (\phi ,\lambda _c(\phi ))=0\)  since this case is equivalent to a Boolean
model.
